ADMM for Exploiting Structure in MPC Problems

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Model predictive control (MPC) handles a control task by the recurrent solution of an optimization problem. The resulting computational burden calls for efficient optimization, particularly under cost and performance pressure. As several publications testify, efficiency is improved when the congruence or fit between control hardware, optimization algorithm, and problem structure is high, meaning that these elements are well-adjusted to each other. We consider embedded platforms such as FPG As, and we use the alternating direction method of multipliers (ADMM) as the optimization algorithm. We tailor this setup to MPC -type problems, letting ADMM exploit the problem structure while taking the best of the embedded platform. Most notably, we exploit interacting components in the controlled system by decomposing it into virtual subsystems. The resulting structure-exploiting algorithm shows the following characteristics: (i) it is highly parallelizable, suiting the availability of parallel threads on embedded hardware; (ii) it scales favorably with the problem size; and (iii) even for a single-thread implementation, given that the controlled system is sufficiently structured, it improves overall performance.